Hex Addition Help

I am working on a programming assignment for class and having a little trouble. The biggest trouble I am having is working with arrays and doing the hex calculations, then making the conversion back to decimal.

I have included the assignment description below:

Write a C++ program to perform addtion of two hexadecimal numerals each with up to 10 digits. If the result of the hexadecimal numerals is more than 10 digits long, then simply give the output message "Addition Overflow" and not the result of the addition. Use arrays to store hexadecimal numerals as arrays of characters. Include a loop to repeat this calculation for new numbers until the user says she or he want's to end the program.

I am working on a programming assignment for class and having a little trouble. The biggest trouble I am having is working with arrays and doing the hex calculations, then making the conversion back to decimal.

I have included the assignment description below:

Write a C++ program to perform addtion of two hexadecimal numerals each with up to 10 digits. If the result of the hexadecimal numerals is more than 10 digits long, then simply give the output message "Addition Overflow" and not the result of the addition. Use arrays to store hexadecimal numerals as arrays of characters. Include a loop to repeat this calculation for new numbers until the user says she or he want's to end the program.

It's only an example and you'll have to adjust it to your needs ...
To make the sum of two hexadecimals you could do the following:
> Convert them both to decimal base ...
> Add those two integers ...
> Convert them back to hexadecimal base ...

> If you want to know if there was a so-called 'overflow' you only have to save the result in a string, and use the length() -method to check the number of characters, if it's higher than 10 you print out a message there was an 'OVERFLOW' ...

> You can use the width manipulator to set the output width (= of the result of the addition) to 10 characters ...

I am most confused about the actual conversion from Hex to decimal at the moment.

1. Declare an integer and initialize it to 0.
2. Go through the hex string one character at a time.
2a. Isolate the hex digit and and convert it to an integer in the range of 0 to 15.
2b. Figure out the "place" of that hex integer (i.e. 1, 16, 256, 4096, etc.).
2c. Multiply 2a times 2b.
2d. Add 2c to the integer declared in step 1.
2e. Repeat 2a through 2d for the next hex digit.